Exercício de Dinamica (99)

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110 
 
 
PROBLEM 11.78 
A car is traveling at a constant speed of 
54 km/h when its driver sees a child run into 
the road. The driver applies her brakes until 
the child returns to the sidewalk and then 
accelerates to resume her original speed of 
54 km/h; the acceleration record of the car is 
shown in the figure. Assuming 0x = when 
t 0,= determine (a) the time t1 at which the 
velocity is again 54 km/h, (b) the position of 
the car at that time, (c) the average velocity of 
the car during the interval 1 1s .t t≤ ≤ 
 
SOLUTION 
Given: At 0, 0, 54 km/h;t x v= = = 
 For 1,t t= 54 km/hv = 
First note 54 km/h 15 m/s= 
(a) We have b av v= + (area under a t− curve from at to )bt 
 Then at 2 s:t = 15 (1)(6) 9 m/sv = − = 
 4.5 s:t = 
1
9 (2.5)(6) 1.5 m/s
2
v = − = 
 1:t t= 1
1
15 1.5 ( 4.5)(2)
2
t= + − 
 or 1 18.00 st = 
(b) Using the above values of the velocities, the v t− curve is drawn as shown.